Rewrite as a simplified fraction. ${0.8\overline{82} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 882.8282...\\ 10x &= 8.8282...\end{align*}}$ Subtracting the two equations, we have: ${990x = 874}$ ${x = \dfrac{874}{990}} $ ${x = \dfrac{437}{495}} $